How do you make a light streak like this one on Blender Internal?
To animate the streak, create two curve objects. Shape the first one to be the shape of the extrusion, the second as the path that it will follow.

In the curve settings for the path select the other curve to be the Bevel Object, then animate the start and end of the bevel factor. You could also add a solidify modifier to get some thickness to the shape.





As a starting point for the material, you want to have it emit a little and to be mostly transparent, you can add a texture to get the striped variation in transparency. For cycles use a mix node with an emission and a tranparent node.



Add a glow in the compositor to finish off the effect, maybe some motion blur as well.